Question

Isabella's parents are starting acollege fund for her today, onher fifth birthday. Assumingthey make no additional depositsor withdrawals, if they want togive her 50 000 Brazilian Realon her eighteenth birthday,how much do they need to deposit now if the bank isoffering an interest rate of 5.5%,compounded monthly. Roundyour answer to the nearestwhole number.

Answer 1

Today Isabella is having her 5th birthday and her parents want to make one single deposit now so they can collect a total of 50000 Brazilian Real when she is 18.

The investment is thought to be for n=13 years.

The present value (PV) and the future value (FV) of the investment can be calculated by using the compound interest's formula:

`FV=PV(1+(r)/(m))^(n\cdot m)`

Where r is the interest rate (APR) offered by the bank, m is the number of compounding periods by each year. Since the compounding period is monthly, then m=12.

If we are given the final value and we want to calculate the present value, then the formula is:

`PV=FV(1+(r)/(m))^(-n\cdot m)`

Substituting:

`PV=50000(1+(0.055)/(12))^(-13\cdot12)`

Calculating:

`\begin{gathered} PV=50000(1.0045833)^(-156) \\ PV=50000\cdot0.49 \\ PV=24499.59 \end{gathered}`

Isabella's parents should deposit near 24500 Brazilian Reals today